Comparation of Numerical Methods for Calculation of Thin Slabs

2014 ◽  
Vol 969 ◽  
pp. 73-77 ◽  
Author(s):  
Oldrich Sucharda ◽  
Jan Kubosek
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Concrete Slabs ◽  
The Finite Element Method ◽  
Thin Slab ◽  
Calculation Methods ◽  
Element Mesh ◽  
Internal Forces ◽  
The Finite Difference Method ◽  
Element Method

The purpose of this paper is to compare calculation of internal forces and deformations of slabs for two calculation methods: the finite element method and the finite difference method. Two concrete slabs have been analysed. In the case of the finite element method, different element mesh are used, providing, thus, solutions in different variants. The calculation and algorithms is based on a thin slab theory. Variants calculate in program Scia Engineer effects of shearing forces by means of the Midlins theory or thin slab theory. Algorithms for the calculation were developed in Matlab.

scholarly journals Calculation of the goffered multilayered composite cylindrical shells by using the finite element method

1999 ◽  
Vol 21 (2) ◽  
pp. 116-128
Author(s):  
Pham Thi Toan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
The Finite Element Method ◽  
Multilayered Composite ◽  
Internal Forces ◽  
External Loads ◽  
Element Method ◽  
Composite Cylindrical Shells

In the present paper, the goffered multilayered composite cylindrical shells is directly calculated by finite element method. Numerical results on displacements, internal forces and moments are obtained for various kinds of external loads and different boundary conditions.

Analysis by the mixed method of statically indeterminate frames with elements of increased rigidity and numerical verification of the calculation results using the finite element method

2021 ◽  
Vol 14 (2) ◽  
pp. 54-66
Author(s):  
Svetlana Sazonova ◽  
Viktor Asminin ◽  
Alla Zvyaginceva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Initial Data ◽  
Mixed Method ◽  
Numerical Verification ◽  
Bending Moments ◽  
The Finite Element Method ◽  
Calculation Results ◽  
Internal Forces ◽  
Element Method

The sequence of application of the mixed method for calculating internal forces in statically indeterminate frames with elements of increased rigidity is given. The main system is chosen for the frame with one kinematic and one force unknown. The canonical equations of the mixed method are written, taking into account their meaning. Completed the construction of the final diagram of the bending moments and all the necessary calculations and checks. When calculating integrals, Vereshchagin's rule is applied. The solution of the problem is checked by performing the calculation using the computer program STAB12.EXE; the results of the calculations are numerically verified using the finite element method. An example of the formation of the initial data for the STAB12.EXE program and the subsequent processing of the calculation results, the rules for comparing the numerical results and the results obtained in the calculation of the frame by the mixed method are given.

A Discussion on natural strain and geological structure - The finite element method and the solution of some geophysical problems

1976 ◽  
Vol 283 (1312) ◽  
pp. 139-151 ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Geological Structure ◽  
The Finite Element Method ◽  
Recent Developments ◽  
Limited Application ◽  
Discrete Problems ◽  
The Finite Difference Method ◽  
Made In ◽  
Element Method

The finite element method has become established as a powerful tool for the solution of many problems of continuum mechanics where its physical interpretation, by analogy with discrete problems of structural analysis permits the user to exercise a considerable degree of insight and judgement in its use. Further it is now a recognized mathematical procedure of approximation which embraces many older methodologies (such as the finite difference method) as a subclass. In the field of geological studies its impact is fairly recent and only a limited application has been made to date. The techniques used here have been limited to those established over a decade ago in the parallel fields and recent developments and possibilities barely touched upon. In this paper the author therefore attempts to ( a ) outline some of the general mathematical and practical aspects of the method with illustrations from various fields which are relevant to geological problems, ( b ) survey accomplishments already made in geology and geotechnical fields, and ( c ) suggest some possible new extensions of application.

scholarly journals The Finite Element Method Applied to the Magnetostatic and Magnetodynamic Problems

2020 ◽  
Author(s):  
Dang Quoc Vuong ◽  
Bui Minh Dinh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electric Fields ◽  
Complex Geometry ◽  
Analytic Method ◽  
The Finite Element Method ◽  
Electromagnetic Problems ◽  
Common Technique ◽  
The Finite Difference Method ◽  
Element Method

Modelling of realistic electromagnetic problems is presented by partial differential equations (FDEs) that link the magnetic and electric fields and their sources. Thus, the direct application of the analytic method to realistic electromagnetic problems is challenging, especially when modeling structures with complex geometry and/or magnetic parts. In order to overcome this drawback, there are a lot of numerical techniques available (e.g. the finite element method or the finite difference method) for the resolution of these PDEs. Amongst these methods, the finite element method has become the most common technique for magnetostatic and magnetodynamic problems.

COMPUTATIONAL CONTACT MECHANICS BASED ON THE rp-VERSION OF THE FINITE ELEMENT METHOD

2011 ◽  
Vol 08 (03) ◽  
pp. 493-512 ◽  
Author(s):  
DAVID FRANKE ◽  
ERNST RANK ◽  
ALEXANDER DÜSTER
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
The Finite Element Method ◽  
Problem Size ◽  
Element Mesh ◽  
Polynomial Degree ◽  
Adaptive Discretization ◽  
Loss Of Regularity ◽  
Element Method

In this paper we present an rp-adaptive discretization strategy to perform unilateral two-dimensional (2D) mechanical contact simulations by combining the r- and p-versions of the finite element method (FEM). The p-version leaves the finite element mesh unchanged and increases the shape function's polynomial degree in order to obtain convergence toward the exact solution of the underlying mathematical model. The r-method relocates nodes of an existing FE-mesh to improve the discretization of a given problem without introducing additional degrees of freedom, therefore, keeping the problem size fixed. The rp-version, which is a combination of the two aforementioned methods, is used in our study to move a node of the FE-mesh to the end of the contact zone to account for the loss of regularity that arises due to the change from contact to noncontact along the edge. It will be shown that highly accurate results can be obtained by using high-order (p) finite elements in combination with the penalty method and a relocation (r) of element nodes.

scholarly journals Advanced Design of Block Shear Failure

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1088
Author(s):  
Marta Kuříková ◽  
David Sekal ◽  
František Wald ◽  
Nadine Maier
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Failure ◽  
Plate Thickness ◽  
Design Procedure ◽  
The Finite Element Method ◽  
Initial Stiffness ◽  
Block Shear ◽  
Internal Forces ◽  
Element Method

This paper presents the behaviour and design procedure of bolted connections which tend to be sensitive to block shear failure. The finite element method is employed to examine the block shear failure. The research-oriented finite element method (RFEM) model is validated with the results of experimental tests. The validated model is used to verify the component-based FEM (CBFEM) model, which combines the analysis of internal forces by the finite element method and design of plates, bolts and welds by the component method (CM). The CBFEM model is verified by an analytical solution based on existing formulas. The method is developed for the design of generally loaded complicated joints, where the distribution of internal forces is complex. The resistance of the steel plates is controlled by limiting the plastic strain of plates and the strength of connectors, e.g., welds, bolts and anchor bolts. The design of plates at a post-critical stage is available to allow local buckling of slender plates. The prediction of the initial stiffness and the deformation capacity is included natively. Finally, a sensitivity study is prepared. The studied parameters include gusset plate thickness and pitch distance.

scholarly journals INVESTIGATION OF THE CARRYING CAPACITY OF REINFORCED CONCRETE SLABS WITH CRACKS AFTER THEIR REINFORCEMENT WITH COMPOSITE FABRICS BY THE FINITE ELEMENT METHOD USING THE PRINS COMPUTER COMPLEX

2019 ◽  
Vol 45 (4) ◽  
pp. 142-152 ◽  
Author(s):  
V. P. Agapov ◽  
K. R. Aydemirov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reinforced Concrete ◽  
Finite Elements ◽  
Concrete Slabs ◽  
The Finite Element Method ◽  
Design Scheme ◽  
Reinforced Concrete Slabs ◽  
Composite Fabrics ◽  
Element Method

Objectives. The finite element method for cracked reinforced concrete slabs analysis after they were reinforced with composite fabrics in order to determine the residual safety factor is considered. Method. The method is based on the use of algorithms for calculating of structures with the account of the geometrical and physical nonlinearities, implemented in the PRINS program. These algorithms assume the use of the same calculation scheme in the process of the problem solving. However, the specifics of the assigned problem is that the design sсheme of the structure before the appearance of defects in it and after its amplification with the help of composite materials should change. Result. Taking into account this circumstance, the algorithms of nonlinear calculation of structures under the PRINS program were supplemented with an option that allows changing the parameters of the design scheme in the process of through calculation. To study the bearing capacity of reinforced concrete slabs, multilayer finite elements are used, for each of which a specific package of materials is specified. Modernization of the design scheme in this case comes down to replacing one package of materials with another. An example of calculation of a slab with a crack reinforced with composite fabric is given. Conclusion. It is shown that the use of a tunable design scheme can significantly improve the accuracy of calculations. In this case, the final result depends on what stage of the formation of defects in the slab its strengthening is realized. The special  multilayered finite elements of a quadrangular shape are used in calculations. The elements consist of four simple triangles, for which most of the matrix characteristics are calculated in a closed form. This is especially important when carrying out nonlinear calculations that require repeated computations of these characteristics. 

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